Why does stress drop after the ultimate point?

The graph uses engineering stress (force divided by original area). During necking the true cross-section shrinks faster than the force drops, so engineering stress typically falls even though true stress may still rise.

Stress–Strain & Hooke’s Law

This lab shows a qualitative engineering stress–strain curve for a ductile metal: σ = Eε in the elastic region until yield, an optional yield plateau, linear strain hardening to the ultimate tensile strength, then a drop in engineering stress during necking until fracture. It is a teaching cartoon, not a calibrated material model.

Who it's for: Intro mechanics of materials and solid mechanics; vocabulary for elastic limit, yield, ultimate, and ductility.

Key terms

Young’s modulus
yield stress
ultimate tensile strength
necking
fracture strain
Hooke’s law

How it works

A qualitative engineering stress–strain curve for a ductile metal: in the elastic region stress is proportional to strain (Hooke’s law, σ = Eε). Beyond the yield point the material flows (here shown as a short plateau), then strain hardening raises stress to the ultimate tensile strength. After the ultimate point, necking makes the engineering stress drop until fracture. Numbers are for illustration — real curves depend on alloy, temperature, and strain rate.

Key equations

Elastic: σ = Eε, ε_y = σ_y/E

Then: yield plateau → hardening to σ_u → necking → σ → 0 at ε_f

Frequently asked questions

Why does stress drop after the ultimate point?: The graph uses engineering stress (force divided by original area). During necking the true cross-section shrinks faster than the force drops, so engineering stress typically falls even though true stress may still rise.

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